The Mathematics Curriculum and Assessment Policy (CAPS) document defines ‘mathematics [as] . . . a human activity’ (DBE, 2011a, p.8). This adoption of a realistic approach to the learning and teaching of mathematics appears to be partial, however, in that at the entry point of the Intermediate Phase, the recommendations of the policy makers are read as prescriptions by practitioners. In particular, the recommendation that ‘as the number range for doing calculations increases up to Grade 6, learners should develop more efficient techniques for calculations, including using columns’ (DBE, 2011b, p.13) is taken as a prescription to push the standard methods as the way to solving (often de-contextualized) problems from the very start of Grade 4, in disregard to the admonition that ‘these techniques should only be introduced and encouraged once learners have an adequate sense of place value and understanding of the properties of numbers and operations’ (DBE, 2011b, p.13). In the background of reports that place South African schools well below international standards with regard to mathematics, with only a third of the learners in grade 3 having attained the minimum standard required of learners at their level in 2011, this report focuses on an exploration into the purported catalytic role that the emergent model of an empty number line can play in shifting learners’ attention from counting (calculation by counting ) towards a focus on the structural properties of number (calculation by structuring). The use of emergent models is meant to support and improve upon learners’ informal solution strategies whilst seeking to reverse what Freudenthal referred to as the “anti-didactical” use of models in a ‘top-down instructional design strategy in which static models are derived from crystallized expert mathematical knowledge’ (Gravemeijer and Stephan, 2002, p.146). With a particular focus on poor performance in numeracy, the Wits Maths Connect-Primary (WMC-P) project was established with the overarching aim of improving the learning and teaching of primary school mathematics. My investigation is located within one Grade 4 class in one of the WMC-P project schools, and in this project, I act as both the teacher of six intervention lessons focused on additive relation problems, as well as researcher of the models and strategies that learners use prior to the intervention lessons, within these lessons, and subsequently. This report presents evidence to illustrate, firstly, that at the entry point of grade 4 level, learners are highly dependent on concrete strategies for solving addition and subtraction problems, and secondly that with proper intervention, learners can make significant shifts towards more abstract calculation. On the one hand, the key finding that the majority of the problems were tackled using tallies in the pre-test confirms what research has observed regarding the tendency for learners to remain highly dependent on concrete strategies at grade 2 (Venkat, 2011) and grade 3 (Ensor et al., 2009). Also, the results indicate a high proportion of incorrect answers resulting from the use of the column model across all questions in the pre-test and the post-test. On the other hand, the imposition of the use of the empty number line in the delayed-post-test points to the fact that improvements can be achieved in relatively short time frames, and importantly, that these improvements can be retained beyond their immediate coverage in class.

by Tan Ah Kiang. / Bibliography: leaves 90-96 / Thesis (M.A.Ed.) -- Chinese University of Hong Kong, 1983

研究者透過課堂學習研究(Learning study, Marton, 2001)，探討「部件識字」的成效，及其對學生識字量的影響，以調整現有的小一語文教學內容及教學法，鞏固學生學習語文的根基。研究分析「部件識字」對學生識字量的影響，以及學生的識字能力能否轉移到閱讀層面。 研究以部件識字法配合變易理論進行，研究團隊設計不同教學內容及活動，透過不同策略，強化學生對「部件識字法」的認識，掌握當中的認字技巧，以提高識字能力。過程中，研究團隊先透過學生於識字前測的表現，診斷出學習難點，再定出課堂學習內容及其關鍵特徵，透過共同備課，聚焦地為特定學習內容設計教學活動。進行教學後，再透過後測檢視學生表現，利用有關數據，就學生的識字能力和識字量作量化分析。 研究結果顯示，「部件識字」對提升學生識字量的成效顯著，學生在掌握字詞形、音、義，書寫及應用字詞的能力上均有進步，亦有利學生進行字詞解碼及提前閱讀，以致識字能力能轉移到閱讀層面，有助提升閱讀能力。 Researchers investigated the effectiveness of the “Component Word Acquisition” and its influence on students’ Repertoire of Word through the Learning Study (Marton, 2001), in order to enhance the existing language teaching content and teaching methods; and to consolidate the foundation of students' language learning. The study will analyze the effect of Component Word Acquisition on students’ Repertoire of Word, and whether their abilities of literacy can be transferred to the reading level. Assisted with the Theory of Variation in addition to Component Word Acquisition, the Research team designed different course contents and activities and a variety of strategies, in order to improve students’ Repertoire of Word and the ability of literacy. Throughout the process, the Research team based on the students’ performance in the literacy ability pre-test to diagnose their difficulties in learning, and then set the learning contents outlines and identified its critical features. Specific teaching activities to the learning content were then tailor-made through collaborative lesson planning. Afterward, the students’ performance was studied through the literacy ability post-test. Data was gathered to perform the quantitative analysis on students’ Repertoire of Word and their abilities of literacy. The study results show that the “Component Word Acquisition” is remarkable to enhance students' Repertoire of Word, and improve their abilities of understanding the words’ forms, pronunciations and meanings, as well as words writing and application. This is also beneficial to students on word decoding, so that their abilities of literacy can be transferred to the reading level and thus to enhance their reading abilities / published_or_final_version / Education / Master / Master of Education

published_or_final_version / Education / Master / Master of Education

published_or_final_version / Education / Master / Master of Philosophy

The researcher's personal conviction that major problems in the teaching of mathematics are inherited from elementary levels inspired the investigation of the contribution of practical work in the teaching of fraction division in grade seven. The all encompassing approach of the study dictated the involvement of teachers and learners as participants. Teachers' perceptions of practical work and their classroom practices were investigated to confirm or refute existing assumptions and literature claims. Questionnaires in which teachers expressed their views on practical work and fraction teaching were administered to teachers. Lessons on the division of fractions were observed to determine teachers' practices in relation to the researcher's assumptions and claims by literature. Data yielded by these research instruments confirmed or refuted assumptions and literature claims. Learners underwent an experiment and their views were sought to establish the value of practical work in the teaching of fractions and fraction division. Instruments used for the experiment were the pre-test, post-test and worksheets. Data from these instruments gave an indication of the value of practical work in enhancing learners' understanding of fraction division. Learners' responses to interview questions further elucidated and confirmed the valuable role played by practical work in learners ' understanding of fraction division. Learners' responses also provided deeper insight into facets of learners ' cognitive development as they engaged with different aspects of practical work in the division of fractions . Besides confirmation and refutation of some established assumptions and literature claims, previously unknown realities about aspects of practical work and fraction division also emerged from findings. This wealth of the data carried crucial implications for teacher training, the teaching of fractions and fraction division, and further research. A look at these implications hopes to contribute to the enhancement and improvement of the teaching of fractions and fraction division. Teacher training institutions, designers of INSET programmes, policy makers and teachers should all benefit from findings of this study. / Thesis (M.Ed.)-University of Kwazulu-Natal, 2005.

This study explores how Lesotho primary school teachers understand and interpret problem-solving (PS) and how they teach and support it. Observation schedules and semi-structured interviews were used to collect data from classrooms, teachers and learners. The findings revealed that teachers have considerable understanding of (PS) and value it but are not teaching it. Teachers attribute this to their lack of knowledge, the difficult conditions in their schools, policy constraints (such as assessment) and their own habits and behaviours. However, the data also indicated that teachers, with support, can successfully design and teach appropriate lessons in their schools, raising issues about their knowledge, beliefs, identity and structures. / Theses (Ph.D.)-University of KwaZulu-Natal, Durban, 2005.

The purpose of this study was to determine teacher engagement with HIV/AIDS education in primary school. Since the emergence and acknowledgement of the HIV/AIDS epidemic in South Africa, the national education department's policy has advanced HIV/AIDS education as a priority. The new curriculum has opened up opportunities for HIV/AIDS education to be inserted in the curriculum especially in the learning area Life Orientation in the primary school, which previously did not exist. There is a paucity of research documenting teachers' experiences on the implementation of the HIV/AIDS curriculum. The manner in which teachers engage with the HIV/AIDS curriculum is not known. This study focused on 9 teachers in the intermediate and senior phases in a particular primary school in KwaZulu Natal who have had experience in the implementation of the HIV/AIDS curriculum over the past four years in their school. A survey questionnaire was administered to all educators in the study. The three intermediate educators participated in face-to-face interviews as well as a focus group discussion. An interview was conducted with the member of the management team who was part of the sample. The results from the survey, interviews and focus group discussion suggest that teachers were strongly implementing the HIV/AIDS curriculum in their classrooms while experiencing some practical challenges. This study also suggests that the educators found the Department Of Education's implementation plan suppressive. All three intermediate phase teachers used creative methods to assist in the implementation of the curriculum. The respondents claimed that the workshops and meetings that they had attended were invaluable to them. They however preferred seeing the community more closely involved in the fight against HIV/AIDS, as this was not an issue confined to the school exclusively. Teachers would also liked to have had HIV/AIDS education implemented across the curriculum, as the task to empower learners in this regard was a mammoth one. The unique and challenging experiences of teachers implementing the HIV/AIDS curriculum must be documented before any theoretical positions can be articulated about the implementation of HIV/AIDS education in primary schools in South Africa. This study has contributed to research on the implementation of HIV/AIDS education in primary school by providing some insight into a group of educators' experiences. / Thesis (M.Ed.) - University of KwaZulu-Natal, Durban, 2004.

This study sought to explore teachers' experiences in teaching Mathematics and Science through second language in Standard 4 at rural primary schools in Lesotho. In addressing this purpose, a qualitative case study method of data production was used. The participants were four Standard 4 Mathematics and Science teachers from three selected schools. Qualitative data were collected through individual semi-structured interviews and lesson observations in the classroom. These were analyzed using a qualitative thematic approach. The study is informed by Vygotsky‟s social constructivist theory and Shulman‟s pedagogical content knowledge theory. The findings revealed that teachers experienced several challenges in teaching Mathematics and Science through second language in a transitional class. The greatest challenge that the participants experienced was the language that is used for instruction in Standard 4. According to the Educational Policy of the Government of Lesotho, English has been approved as the medium of instruction (MOI) from Standard 4 upwards. In Standards 1-3 pupils are taught in their mother tongue (Sesotho); thereafter the MOI changes to English. The participants reported that the shift from Sesotho to English posed a serious problem in the teaching and learning of Mathematics and Science in Standard 4. They further claimed that most pupils in Standard 4 do not proceed to the next class, since these two subjects are core subjects and the MOI makes passing them problematic. Teachers regularly employed code-switching as a strategy to make meaning for their pupils in their classrooms. It is recommended that the Government of Lesotho should consider changing the medium of instruction to English from Standard 1. It is also recommended that the inspectorate service should be decentralised and that one teacher at primary level should not teach all the subjects but teach according to specialisation. There should also be more regular in-service training of Mathematics and Science teachers. / Thesis (M.Ed.) - University of KwaZulu-Natal, Edgewood, 2011.

The dire need for capacitating Economic and Management Sciences (EMS) educators in subject-specific knowledge occurred to me whilst conducting workshops for EMS educators within the KwaZulu-Natal Department of Education. Educators often complained that they neglected EMS as a Learning Area as they lacked the requisite subject~specific knowledge. This, they claimed was exacerbated by the paucity of EMS educator and learner support materials. This prompted me to undertake a case study of the current capacity building strategies of heads of department, curriculum co-ordinators and level 1 educators in (EMS) Learning Area. The case study was restricted to a cluster of 5 pnmary schools in the Ethekwini Region of the Kwa-Zulu Natal Department of Education. Schools were chosen on the basis of convenience, cost, proximity to each other and previous professional involvement with the schools. Data were collected through questionnaires, interviews and observation at workshops. Findings suggest that there existed a lack of fundamental knowledge in the EMS learning area and further that current development strategies did not necessarily meet the needs of educators. Stemming from the research findings, the study recommends that continuous professional development of educators must be seen as an evolving set of activities that should respond to the specific contextual needs of educators at different stages in their lifelong development as professionals. / Thesis (M.Ed.)-University of KwaZulu-Natal, Durban, 2005.